Modeling of laser-induced damage in KDP crystals

Transcription

1 Modeling of laser-induced damage in KDP crystals Guillaume Duchateau and Ludovic Hallo CEA, Centre d Etudes du Ripault, BP6, 76 Monts CELIA, 5 Cours de la Libération, 45 Talence KDP crystals frequency converters for LMJ (ns) or fs laser facilities Damage is observed need to understanding the physical mechanisms leading to damage KDP : K + + H PO 4 - K Modelisation precursor defect in the nanometric scale Absorption modeling (plasma creation and expansion, Mie theory) Resolution of Fourier and hydrodynamics equations (D-axisymmetric code CHIC) Determination of the damage morphology and comparison to experiments Comparison between ns and fs energy deposition Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9//

2 Defects in KDP crystals UV/IR H O P Radical A : [HPO 4 ] - Radical B : [H PO 4 ] J.A.McMilan J.Chem.Phys. 68,No.8, 978 H PO - 4 [H PO 4 ] + é (chauds) H PO - 4 recombination é-hole 8 nm Free electrons CB [HPO 4 - ] + H é capture by H + H mobility in the lattice Structural defect (cracks, dislocations, ) Processus Processus VB G. Geoffroy and S. Guizard fs time-resolved interferometry experiment A few states located in the band gap strongly enhance the MPI cross section Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9//

3 Modelisation UV/IR Plasma creation : Plasma heating Q Q ( a / λ, n k) = Mie theory abs abs, A density close to the critical plasma density is assumed to be produced in a time much shorter than the pulse duration a = nm Hydrodynamics Numerical resolution of Fourier and hydrodynamics equations (D-axisymmetric code CHIC) EOS Perfect Gas if T > K fs energy deposition : the energy absorbed by the defect in the ns regime is used as initial condition (energy deposition and hydrodynamics are decorrelated) Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9//

4 Damage phenomenology Pressure Density A shock wave is created Cavity creation due to the rarefaction wave The shock propagates over large distances Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9// 4

5 Temperature [K] 5 Density 5 Pressure [GPa],5,5 (a) (b) (c) ns energy deposition : time evolution of the relevant physical quantities F = 6 J/cm τ = ns t = ps t = ps t = ps t = 4 ps t = 5 ps Radius [nm] Pressure [GPa] Density (a) (c) Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9// 5 Temperature [K] Cavity radius [nm] (b) (d) T exp = K C.W. Carr et al, Phys. Rev. Lett. 9, 874 (4) Conclusions A shock wave is created at the beginning of the interaction P = 4 GPa Cavity creation T = K at the end of the pulse

6 ns energy deposition : pressure profiles at large distances 9 5 ps 5 ps Pressure [Pa] 8 7 ns ns The pulse is switched off ns 4 ns 5 ns 6 ns 7 ns 8 ns 9 ns ns ns Radius [micron] Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9// 6

7 ns energy deposition : density variations profiles Relative density variation,,,, ns 4 ns 5 ns Relative density variation Cavity 4 5 Radius [micron] 6 ns 7 ns 8 ns 9 ns ns ns Damage criterion e-5 e Radius [micron] Conclusions Damage size = microns < - distinct regions C.W. Carr et al, Appl. Phys. Lett. 89, 9 (6) Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9// 7

8 ns energy deposition : damage morphology Laser absorption Damage morphology. Cavity : ~µm. Compacted and melted shell : ~ µm. A larger outer region slightly shocked : ~ µm C.W. Carr et al, Appl. Phys. Lett. 89, 9 (6) Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9// 8

9 ns energy deposition : come back on the energy deposition.4 Absorption coefficient Q abs... Conclusions Q abs decreases due to the plasma dilution The absorbed power is mainly constant.7 Absorbed power [W].65.6 E abs = nj Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9// 9

10 Pressure [GPa] Density fs energy deposition : time evolution of the relevant physical quantities E abs (t=) = nj in order to compare to the ns energy deposition a = nm fs energy deposition Temperature [K] Cavity radius [nm] fs pulse ns pulse Conclusions and comparison Same phenomenology as ns T = K P = 5 GPa Same cavity Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9// Pressure [GPa] Density (a) (c) 4 ns energy deposition Temperature [K] Cavity radius [nm] (b) (d)

11 fs and ns damage morphologies ns energy deposition : ~ µm : ~ µm : ~ µm Relative density variation,,,,,, fs energy deposition : ~ µm : ~4 µm : ~65 µm, e Distance [microns] Same morphology but different proportions Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9//

12 Summary and outlooks ns energy deposition (comparison to experiments) From 5 nm to 5 µm (x) A shock is created at the beginning of the interaction T = cte = K Complex morphology : regions fs energy deposition (predictions) Mainly same phenomenology as the ns regime but with higher T and P For the same amount of energy, the damage morphology is similar The cavity formation is mainly driven by the total absorbed energy Outlooks Anisotropy realistic EOS Acknowledgments : L. Hallo, G. Geoffroy, S. Guizard, J. Breil, G. Schurtz, V. Tikhonchuk, D. Hébert Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9//

13 ns energy deposition : influence of the laser fluence 5 (a) 5 4 (b) T max [K] 5 5 P max [GPa] P max [GPa] Fluence [J/cm ] 5 (c) 4 Damage size [µm] T max [K] Fluence [J/cm ] 45 4 (d) Fluence [J/cm ] Workshop Modélisation et procédés ultra-brefs, Carry-Le-Rouet 9//